Scaling properties of the action in the Riemann-Liouville fractional standard map.

The Riemann-Liouville fractional standard map (RL-fSM) is a two-dimensional nonlinear map with memory given in action-angle variables (I,θ). The RL-fSM is parameterized by K and α∈(1,2], which control the strength of nonlinearity and the fractional order of the Riemann-Liouville derivative, respectively. In this work we present a scaling study of the average squared action 〈I^{2}〉 of the RL-fSM along strongly chaotic orbits, i.e., for K≫1. We observe two scenarios depending on the initial action I_{0}, I_{0}≪K or I_{0}≫K. However, we can show that 〈I^{2}〉/I_{0}^{2} is a universal function of the scaled discrete time nK^{2}/I_{0}^{2} (n being the nth iteration of the RL-fSM). In addition, we note that 〈I^{2}〉 is independent of α for K≫1. Analytical estimations support our numerical results.

Ningalins, Pyrrole-Bearing Metabolites Isolated from Didemnum spp. Synthesis and MDR-Reversion Activity in Cancer Therapy.

Multi-Drug Resistance (MDR) is one of the most frequent problems observed in the course of cancer chemotherapy. Cells under treatment, tend to develop survival mechanisms to drug-action thus generating drug-resistance. One of the most important mechanism to get it is the over expression of P-gp glycoprotein, which acts as an efflux-pump releasing the drug outside of the cancer cell. A strategy for a succesfull treatment consists in the co-administration of one compound that acts against P-gp and another which acts against the cell during chemotherapy. Ningalins are pyrrole-containing naturally occurring compounds isolated mainly from the marine tunicate Didemnum spp and also they are some of the top reversing agents in MDR treatment acting on P-gp. Considering the relevance displayed for some of these isolated alkaloids or their core as a drug for co-administration in cancer therapy, all the total synthesis described to date for the members of ningalins family are reviewed herein.

Characterizing a transition from limited to unlimited diffusion in energy for a time-dependent stochastic billiard.

We explore Fermi acceleration in a stochastic oval billiard which shows unlimited to limited diffusion in energy when passing from the free to the dissipative case. We provide evidence for a transition from limited to unlimited energy growth taking place while detuning the corresponding restitution coefficient responsible for the degree of dissipation. A corresponding order parameter is suggested, and its susceptibility is shown to diverge at the critical point. We show that this order parameter is also be applicable to the periodically driven oval billiard and discuss the elementary excitation of the controlled diffusion process.

Ten-Year Follow-up of 9-Valent Human Papillomavirus Vaccine: Immunogenicity, Effectiveness, and Safety.

BACKGROUND AND OBJECTIVES: The 9-valent human papillomavirus (9vHPV) vaccine Phase III immunogenicity study in 9- to 15-year-old boys and girls was extended to assess immunogenicity and effectiveness through 10 years after the last vaccine dose (NCT00943722). METHODS: Boys (n = 301) and girls (n = 971) who received three 9vHPV vaccine doses in the base study (day 1, months 2 and 6) enrolled in the extension. Serum was collected through month 126 for antibody assessments by competitive Luminex immunoassay and immunoglobulin G-Luminex immunoassay. For effectiveness analysis starting at age 16 years, genital swabs were collected (to assess HPV DNA by polymerase chain reaction) and external genital examinations conducted every 6 months. Primary analyses were conducted in per-protocol populations. RESULTS: Geometric mean antibody titers peaked around month 7, decreased sharply between months 7 and 12, then gradually through month 126. Seropositivity rates remained ≥81% by competitive Luminex immunoassay and ≥95% by immunoglobin G-Luminex immunoassay at month 126 for each 9vHPV vaccine type. After up to 11.0 (median 10.0) years of follow-up postdose 3, there were no cases of HPV6/11/16/18/31/33/45/52/58-related high-grade intraepithelial neoplasia or condyloma in males or females. Incidence rates of HPV6/11/16/18/31/33/45/52/58-related 6-month persistent infection in males and females were low (54.6 and 52.4 per 10000 person-years, respectively) and within ranges expected in vaccinated cohorts, based on previous human papillomavirus vaccine efficacy trials. CONCLUSIONS: The 9vHPV vaccine demonstrated sustained immunogenicity and effectiveness through ∼10 years post 3 doses of 9vHPV vaccination of boys and girls aged 9 to 15 years.

Metformin, a biological and synthetic overview.

Metformin is the most widely known anti-hyperglycemic, officially acquired by the USA government in 1995 and in 2001 it became the most prescribed treatment for type II diabetes. But how did it become the must-use drug for this disease in such a short period of time? it all started with traditional medicine, by using a plant known as "goat's rue" for the reduction of blood glucose levels. Its use arose in 1918 and evolved to the metformin synthesis in laboratories a couple of years later, using very rudimentary methods which involved melting and strong heating. Thus, a first synthetic route that allowed the preparation of the initial metformin derivates was established. Some of these resulted toxics, and others outperformed the metformin, reducing the blood glucose levels in such efficient way. Nevertheless, the risk and documented cases of lactic acidosis increased with metformin derivatives like buformin and phenformin. Recently, metformin has been widely studied, and it has been associated and tested in the treatment of type II diabetes, cancer, polycystic ovarian syndrome, cell differentiation to oligodendrocytes, reduction of oxidative stress in cells, weight reduction, as anti-inflammatory and even in the recent COVID-19 disease. Herein we briefly review and analyze the history, synthesis, and biological applications of metformin and its derivates.

Application of the Slater criteria to localize invariant tori in Hamiltonian mappings.

We investigate the localization of invariant spanning curves for a family of two-dimensional area-preserving mappings described by the dynamical variables I and θ by using Slater's criterion. The Slater theorem says there are three different return times for an irrational translation over a circle in a given interval. The returning time, which measures the number of iterations a map needs to return to a given periodic or quasi periodic region, has three responses along an invariant spanning curve. They are related to a continued fraction expansion used in the translation and obey the Fibonacci sequence. The rotation numbers for such curves are related to a noble number, leading to a devil's staircase structure. The behavior of the rotation number as a function of invariant spanning curves located by Slater's criterion resulted in an expression of a power law in which the absolute value of the exponent is equal to the control parameter γ that controls the speed of the divergence of θ in the limit the action I is sufficiently small.

Information geometry theory of bifurcations? A covariant formulation.

The conventional local bifurcation theory (CBT) fails to present a complete characterization of the stability and general aspects of complex phenomena. After all, the CBT only explores the behavior of nonlinear dynamical systems in the neighborhood of their fixed points. Thus, this limitation imposes the necessity of non-trivial global techniques and lengthy numerical solutions. In this article, we present an attempt to overcome these problems by including the Fisher information theory in the study of bifurcations. Here, we investigate a Riemannian metrical structure of local and global bifurcations described in the context of dynamical systems. The introduced metric is based on the concept of information distance. We examine five contrasting models in detail: saddle-node, transcritical, supercritical pitchfork, subcritical pitchfork, and homoclinic bifurcations. We found that the metric imposes a curvature scalar R on the parameter space. Also, we discovered that R diverges to infinity while approaching bifurcation points. We demonstrate that the local stability conditions are recovered from the interpretations of the curvature R, while global stability is inferred from the character of the Fisher metric. The results are a clear improvement over those of the conventional theory.

Safety and Efficacy of a Third Dose of BNT162b2 Covid-19 Vaccine.

BACKGROUND: Active immunization with the BNT162b2 vaccine (Pfizer-BioNTech) has been a critical mitigation tool against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection during the coronavirus disease 2019 (Covid-19) pandemic. In light of reports of waning protection occurring 6 months after the primary two-dose vaccine series, data are needed on the safety and efficacy of offering a third (booster) dose in persons 16 years of age or older. METHODS: In this ongoing, placebo-controlled, randomized, phase 3 trial, we assigned participants who had received two 30-µg doses of the BNT162b2 vaccine at least 6 months earlier to be injected with a third dose of the BNT162b2 vaccine or with placebo. We assessed vaccine safety and efficacy against Covid-19 starting 7 days after the third dose. RESULTS: A total of 5081 participants received a third BNT162b2 dose and 5044 received placebo. The median interval between dose 2 and dose 3 was 10.8 months in the vaccine group and 10.7 months in the placebo group; the median follow-up was 2.5 months. Local and systemic reactogenicity events from the third dose were generally of low grade. No new safety signals were identified, and no cases of myocarditis or pericarditis were reported. Among the participants without evidence of previous SARS-CoV-2 infection who could be evaluated, Covid-19 with onset at least 7 days after dose 3 was observed in 6 participants in the vaccine group and in 123 participants in the placebo group, which corresponded to a relative vaccine efficacy of 95.3% (95% confidence interval, 89.5 to 98.3). CONCLUSIONS: A third dose of the BNT162b2 vaccine administered a median of 10.8 months after the second dose provided 95.3% efficacy against Covid-19 as compared with two doses of the BNT162b2 vaccine during a median follow-up of 2.5 months. (Funded by BioNTech and Pfizer; C4591031 ClinicalTrials.gov number, NCT04955626.).

Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well.

We study the dynamics of classical particles confined in a time-dependent potential well. The dynamics of each particle is described by a two-dimensional nonlinear discrete mapping for the variables energy en and phase ϕn of the periodic moving well. We obtain the phase space and show that it contains periodic islands, chaotic sea, and invariant spanning curves. We find the elliptic and hyperbolic fixed points and discuss a numerical method to obtain them. We study the dispersion of the initial conditions after a single iteration. This study allows finding regions where multiple reflections occur. Multiple reflections happen when a particle does not have enough energy to exit the potential well and is trapped inside it, suffering several reflections until it has enough energy to exit. We also show deformations in regions with multiple reflection, but the area remains constant when we change the control parameter NC. Finally, we show some structures that appear in the e0e1 plane by using density plots.

Efficacy, immunogenicity, and safety of a quadrivalent HPV vaccine in men: results of an open-label, long-term extension of a randomised, placebo-controlled, phase 3 trial.

BACKGROUND: The quadrivalent human papillomavirus (HPV) vaccine was shown to prevent infections and lesions related to HPV6, 11, 16, and 18 in a randomised, placebo-controlled study in men aged 16-26 years. We assessed the incidences of external genital warts related to HPV6 or 11, and external genital lesions and anal dysplasia related to HPV6, 11, 16, or 18, over 10 years of follow-up. METHODS: The 3-year base study was an international, multicentre, double-blind, randomised, placebo-controlled trial done at 71 sites in 18 countries. Eligible participants were heterosexual men (aged 16-23 years) or men who have sex with men (MSM; aged 16-26 years). Men who had clinically detectable anogenital warts or genital lesions at screening that were suggestive of infection with non-HPV sexually transmitted diseases, or who had a history of such findings, were excluded. Eligible participants were randomly assigned (1:1) to receive three doses of either quadrivalent HPV vaccine or placebo on day 1, month 2, and month 6, administered as a 0·5-mL injection into the deltoid muscle. The 7-year, open-label, long-term follow-up extension study was done at 46 centres in 16 countries. Participants who received one or more doses of the quadrivalent HPV vaccine in the base study were eligible for enrolment into the long-term follow-up study (early vaccination group). Placebo recipients were offered the three-dose quadrivalent HPV vaccine at the end of the base study; those who received one or more quadrivalent HPV vaccine doses were eligible for enrolment into the long-term follow-up study (catch-up vaccination group). The primary efficacy endpoints were the incidence of external genital warts related to HPV6 or 11 and the incidence of external genital lesions related to HPV6, 11, 16, or 18 in all participants and the incidence of anal intraepithelial neoplasia (including anal warts and flat lesions) or anal cancer related to HPV6, 11, 16, or 18 in MSM only. The primary efficacy analysis was done in the per-protocol population for the early vaccination group, which included participants who received all three vaccine doses, were seronegative at day 1 and PCR-negative from day 1 through month 7 of the base study for the HPV type being analysed, had no protocol violations that could affect evaluation of vaccine efficacy, and had attended at least one visit during the long-term follow-up study. For the catch-up vaccination group, efficacy was assessed in the modified intention-to-treat population, which included participants who had received at least one vaccine dose, were seronegative and PCR-negative for HPV types analysed from day 1 of the base study to the final follow-up visit before receiving the quadrivalent HPV vaccine, and had at least one long-term follow-up visit. Safety was assessed in all randomised participants who received at least one vaccine dose. This study is registered with ClinicalTrials.gov, NCT00090285. FINDINGS: Between Aug 10, 2010, and April 3, 2017, 1803 participants were enrolled in the long-term follow-up study, of whom 936 (827 heterosexual men and 109 MSM) were included in the early vaccination group and 867 (739 heterosexual men and 128 MSM) were included in the catch-up vaccination group. Participants in the early vaccination group were followed up for a median of 9·5 years (range 0·1-11·5) after receiving the third dose of the quadrivalent HPV vaccine, and participants in the catch-up vaccination group were followed up for a median of 4·7 years (0·0-6·6) after receiving the third dose. In early vaccine group participants during long-term follow-up compared with the placebo group in the base study, the incidence per 10 000 person-years of external genital warts related to HPV6 or 11 was 0·0 (95% CI 0·0-8·7) versus 137·3 (83·9-212·1), of external genital lesions related to HPV6, 11, 16, or 18 was 0·0 (0·0-7·7) versus 140·4 (89·0-210·7), and of anal intraepithelial neoplasia or anal cancer related to HPV6, 11, 16, or 18 in MSM only was 20·5 (0·5-114·4) versus 906·2 (553·5-1399·5). Compared with during the base study (ie, before quadrivalent HPV vaccine administration), during the long-term follow-up period, participants in the catch-up vaccination group had no new reported cases of external genital warts related to HPV6 or 11 (149·6 cases per 10 000 person-years [95% CI 101·6-212·3] vs 0 cases per 10 000 person-years [0·0-13·5]) or external genital lesions related to HPV6, 11, 16, or 18 (155·1 cases per 10 000 person-years [108·0-215·7] vs 0 cases per 10 000 person-years [0·0-10·2]), and a lower incidence of anal intraepithelial neoplasia or anal cancer related to HPV6, 11, 16, or 18 (886·0 cases per 10 000 person-years [583·9-1289·1] vs 101·3 cases per 10 000 person-years [32·9-236·3]). No vaccine-related serious adverse events were reported. INTERPRETATION: The quadrivalent HPV vaccine provides durable protection against anogenital disease related to HPV6, 11, 16, and 18. The results support quadrivalent HPV vaccination in men, including catch-up vaccination. FUNDING: Merck Sharp & Dohme.

Investigation of pollen release by poricidal anthers using mathematical billiards.

Buzz pollination is described using a mathematical model considering a billiard approach. Applications to a rough morphology of a typical poricidal anther of a tomato flower (Solanum lycopersicum) experiencing vibrations applied by a bumblebee (Bombus terrestris) are made. The anther is described by a rectangular billiard with a pore on its tip while the borders are perturbed by specific oscillations according to the vibrational properties of the bumblebee. Pollen grains are considered as noninteracting particles that can escape through the pore. Our results not only recover some observed data but also provide a possible answer to an open problem involving buzz pollination.

Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine through 6 Months.

BACKGROUND: BNT162b2 is a lipid nanoparticle-formulated, nucleoside-modified RNA vaccine encoding a prefusion-stabilized, membrane-anchored severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) full-length spike protein. BNT162b2 is highly efficacious against coronavirus disease 2019 (Covid-19) and is currently approved, conditionally approved, or authorized for emergency use worldwide. At the time of initial authorization, data beyond 2 months after vaccination were unavailable. METHODS: In an ongoing, placebo-controlled, observer-blinded, multinational, pivotal efficacy trial, we randomly assigned 44,165 participants 16 years of age or older and 2264 participants 12 to 15 years of age to receive two 30-µg doses, at 21 days apart, of BNT162b2 or placebo. The trial end points were vaccine efficacy against laboratory-confirmed Covid-19 and safety, which were both evaluated through 6 months after vaccination. RESULTS: BNT162b2 continued to be safe and have an acceptable adverse-event profile. Few participants had adverse events leading to withdrawal from the trial. Vaccine efficacy against Covid-19 was 91.3% (95% confidence interval [CI], 89.0 to 93.2) through 6 months of follow-up among the participants without evidence of previous SARS-CoV-2 infection who could be evaluated. There was a gradual decline in vaccine efficacy. Vaccine efficacy of 86 to 100% was seen across countries and in populations with diverse ages, sexes, race or ethnic groups, and risk factors for Covid-19 among participants without evidence of previous infection with SARS-CoV-2. Vaccine efficacy against severe disease was 96.7% (95% CI, 80.3 to 99.9). In South Africa, where the SARS-CoV-2 variant of concern B.1.351 (or beta) was predominant, a vaccine efficacy of 100% (95% CI, 53.5 to 100) was observed. CONCLUSIONS: Through 6 months of follow-up and despite a gradual decline in vaccine efficacy, BNT162b2 had a favorable safety profile and was highly efficacious in preventing Covid-19. (Funded by BioNTech and Pfizer; ClinicalTrials.gov number, NCT04368728.).

An approach to the classification of COVID-19 based on CT scans using convolutional features and genetic algorithms.

COVID-19 is a respiratory disease that, as of July 15th, 2021, has infected more than 187 million people worldwide and is responsible for more than 4 million deaths. An accurate diagnosis of COVID-19 is essential for the treatment and control of the disease. The use of computed tomography (CT) has shown to be promising for evaluating patients suspected of COVID-19 infection. The analysis of a CT examination is complex, and requires attention from a specialist. This paper presents a methodology for detecting COVID-19 from CT images. We first propose a convolutional neural network architecture to extract features from CT images, and then optimize the hyperparameters of the network using a tree Parzen estimator to choose the best parameters. Following this, we apply a selection of features using a genetic algorithm. Finally, classification is performed using four classifiers with different approaches. The proposed methodology achieved an accuracy of 0.997, a kappa index of 0.995, an AUROC of 0.997, and an AUPRC of 0.997 on the SARS-CoV-2 CT-Scan dataset, and an accuracy of 0.987, a kappa index of 0.975, an AUROC of 0.989, and an AUPRC of 0.987 on the COVID-CT dataset, using our CNN after optimization of the hyperparameters, the selection of features and the multi-layer perceptron classifier. Compared with pretrained CNNs and related state-of-the-art works, the results achieved by the proposed methodology were superior. Our results show that the proposed method can assist specialists in screening and can aid in diagnosing patients with suspected COVID-19.

Dynamical aspects of a bouncing ball in a nonhomogeneous field.

We study some dynamical properties of a charged particle that moves in a nonhomogeneous electric field and collides against an oscillating platform. Depending on the values of parameters, the system presents (i) predominantly regular dynamics or (ii) structures of chaotic behavior in phase space conditioned to the initial conditions. The localization of the fixed points and their stability are carefully discussed. Average properties of the chaotic sea are investigated under a scaling approach. We show that the system belongs to the same universality class as the Fermi-Ulam model.

Six Month Safety and Efficacy of the BNT162b2 mRNA COVID-19 Vaccine

BackgroundBNT162b2 is a lipid nanoparticle-formulated, nucleoside-modified RNA vaccine encoding a prefusion-stabilized, membrane-anchored SARS-CoV-2 full-length spike protein. BNT162b2 is highly efficacious against COVID-19 and is currently authorized for emergency use or conditional approval worldwide. At the time of authorization, data beyond 2 months post-vaccination were unavailable. MethodsIn an ongoing, placebo-controlled, observer-blinded, multinational, pivotal efficacy study, 44,165 [≥]16-year-old participants and 2,264 12-15-year-old participants were randomized to receive 2 doses, 21 days apart, of 30 {micro}g BNT162b2 or placebo. Study endpoints reported here are vaccine efficacy (VE) against laboratory-confirmed COVID-19 and safety data, both up to 6 months post-vaccination. ResultsBNT162b2 continued to be safe and well tolerated. Few participants had adverse events leading to study withdrawal. VE against COVID-19 was 91% (95% CI 89.0-93.2) through up to 6 months of follow-up, among evaluable participants and irrespective of previous SARS-CoV-2 infection. VE of 86%-100% was seen across countries and in populations with diverse characteristics of age, sex, race/ethnicity, and COVID-19 risk factors in participants without evidence of previous SARS-CoV-2 infection. VE against severe disease was 97% (95% CI 80.3-99.9). In South Africa, where the SARS-CoV-2 variant of concern, B.1.351 (beta), was predominant, 100% (95% CI 53.5, 100.0) VE was observed. ConclusionWith up to 6 months of follow-up and despite a gradually declining trend in vaccine efficacy, BNT162b2 had a favorable safety profile and was highly efficacious in preventing COVID-19. (ClinicalTrials.gov number, NCT04368728)

Leaking of orbits from the phase space of the dissipative discontinuous standard mapping.

We investigate the escape of particles from the phase space produced by a two-dimensional, nonlinear and discontinuous, area-contracting map. The mapping, given in action-angle variables, is parametrized by K and γ which control the strength of nonlinearity and dissipation, respectively. We focus on two dynamical regimes, K<1 and K≥1, known as slow and quasilinear diffusion regimes, respectively, for the area-preserving version of the map (i.e., when γ=0). When a hole of hight h is introduced in the action axis we find both the histogram of escape times P_{E}(n) and the survival probability P_{S}(n) of particles to be scale invariant, with the typical escape time n_{typ}=exp〈lnn〉; that is, both P_{E}(n/n_{typ}) and P_{S}(n/n_{typ}) define universal functions. Moreover, for γ≪1, we show that n_{typ} is proportional to h^{2}/D, where D is the diffusion coefficient of the corresponding area-preserving map that in turn is proportional to K^{5/2} and K^{2} in the slow and the quasilinear diffusion regimes, respectively.

Instantaneous frequencies in the Kuramoto model.

Using the main results of the Kuramoto theory of globally coupled phase oscillators combined with methods from probability and generalized function theory in a geometric analysis, we extend Kuramoto's results and obtain a mathematical description of the instantaneous frequency (phase-velocity) distribution. Our result is validated against numerical simulations, and we illustrate it in cases in which the natural frequencies have normal and Beta distributions. In both cases, we vary the coupling strength and compare systematically the distribution of time-averaged frequencies (a known result of Kuramoto theory) to that of instantaneous frequencies, focusing on their qualitative differences near the synchronized frequency and in their tails. For a class of natural frequency distributions with power-law tails, which includes the Cauchy-Lorentz distribution, we analyze the tails of the instantaneous frequency distribution by means of an asymptotic formula obtained from a power-series expansion.

Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine.

BACKGROUND: Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection and the resulting coronavirus disease 2019 (Covid-19) have afflicted tens of millions of people in a worldwide pandemic. Safe and effective vaccines are needed urgently. METHODS: In an ongoing multinational, placebo-controlled, observer-blinded, pivotal efficacy trial, we randomly assigned persons 16 years of age or older in a 1:1 ratio to receive two doses, 21 days apart, of either placebo or the BNT162b2 vaccine candidate (30 µg per dose). BNT162b2 is a lipid nanoparticle-formulated, nucleoside-modified RNA vaccine that encodes a prefusion stabilized, membrane-anchored SARS-CoV-2 full-length spike protein. The primary end points were efficacy of the vaccine against laboratory-confirmed Covid-19 and safety. RESULTS: A total of 43,548 participants underwent randomization, of whom 43,448 received injections: 21,720 with BNT162b2 and 21,728 with placebo. There were 8 cases of Covid-19 with onset at least 7 days after the second dose among participants assigned to receive BNT162b2 and 162 cases among those assigned to placebo; BNT162b2 was 95% effective in preventing Covid-19 (95% credible interval, 90.3 to 97.6). Similar vaccine efficacy (generally 90 to 100%) was observed across subgroups defined by age, sex, race, ethnicity, baseline body-mass index, and the presence of coexisting conditions. Among 10 cases of severe Covid-19 with onset after the first dose, 9 occurred in placebo recipients and 1 in a BNT162b2 recipient. The safety profile of BNT162b2 was characterized by short-term, mild-to-moderate pain at the injection site, fatigue, and headache. The incidence of serious adverse events was low and was similar in the vaccine and placebo groups. CONCLUSIONS: A two-dose regimen of BNT162b2 conferred 95% protection against Covid-19 in persons 16 years of age or older. Safety over a median of 2 months was similar to that of other viral vaccines. (Funded by BioNTech and Pfizer; ClinicalTrials.gov number, NCT04368728.).

Breast cancer diagnosis from histopathological images using textural features and CBIR.

Currently, breast cancer diagnosis is an extensively researched topic. An effective method to diagnose breast cancer is to use histopathological images. However, extracting features from these images is a challenging task. Thus, we propose a method that uses phylogenetic diversity indexes to characterize images for creating a model to classify histopathological breast images into four classes - invasive carcinoma, in situ carcinoma, normal tissue, and benign lesion. The classifiers used were the most robust ones according to the existing literature: XGBoost, random forest, multilayer perceptron, and support vector machine. Moreover, we performed content-based image retrieval to confirm the classification results and suggest a ranking for sets of images that were not labeled. The results obtained were considerably robust and proved to be effective for the composition of a CADx system to help specialists at large medical centers.

Diffusion phenomena in a mixed phase space.

We show that, in strongly chaotic dynamical systems, the average particle velocity can be calculated analytically by consideration of Brownian dynamics in a phase space, the method of images, and the use of the classical diffusion equation. The method is demonstrated on the simplified Fermi-Ulam accelerator model, which has a mixed phase space with chaotic seas, invariant tori, and Kolmogorov-Arnold-Moser islands. The calculated average velocities agree well with numerical simulations and with an earlier empirical theory.